Efficient motion vector coding for video compression

ABSTRACT

Video coding efficiency is improved by jointly coding the x and y components of motion vectors with a single variable length code. The motion vector components for a block of pixels are predicted based on motion vectors of neighboring blocks of pixels. The predicted x and y components are then jointly coded by assigning a single variable length code corresponding to the pair of components, rather than a separate code for each component. If the x and y components do not have a corresponding entry in the coding table, they are coded with an escape code followed by fixed length codes.

FIELD OF THE INVENTION

The invention relates to video coding, and specifically, to an improved method for coding motion vectors.

BACKGROUND OF THE INVENTION

Full-motion video displays based upon analog video signals have long been available in the form of television. With recent advances in computer processing capabilities and affordability, full-motion video displays based upon digital video signals are becoming more widely available. Digital video systems can provide significant improvements over conventional analog video systems in creating, modifying, transmitting, storing, and playing full-motion video sequences.

Digital video displays include large numbers of image frames that are played or rendered successively at frequencies of between 30 and 75 Hz. Each image frame is a still image formed from an array of pixels based on the display resolution of a particular system. As examples, VHS-based systems have display resolutions of 320×480 pixels, NTSC-based systems have display resolutions of 720×486 pixels, and high-definition television (HDTV) systems under development have display resolutions of 1360×1024 pixels.

The amounts of raw digital information included in video sequences are massive. Storage and transmission of these amounts of video information is infeasible with conventional personal computer equipment. Consider, for example, a digitized form of a relatively low resolution VHS image format having a 320×480 pixel resolution. A full-length motion picture of two hours in duration at this resolution corresponds to 100 gigabytes of digital video information. By comparison, conventional compact optical disks have capacities of about 0.6 gigabytes, magnetic hard disks have capacities of 1–2 gigabytes, and compact optical disks under development have capacities of up to 8 gigabytes.

To address the limitations in storing or transmitting such massive amounts of digital video information, various video compression standards or processes have been established, including MPEG-1, MPEG-2, and H.26X. These video compression techniques utilize similarities between successive image frames, referred to as temporal or interframe correlation, to provide interframe compression in which motion data and error signals are used to encode changes between frames.

In addition, the conventional video compression techniques utilize similarities within image frames, referred to as spatial or intraframe correlation, to provide intraframe compression in which the image samples within an image frame are compressed. Intraframe compression is based upon conventional processes for compressing still images, such as discrete cosine transform (DCT) encoding. This type of coding is sometimes referred to as “texture” or “transform” coding. A “texture” generally refers to a two-dimensional array of image sample values, such as an array of chrominance and luminance values or an array of alpha (opacity) values. The term “transform” in this context refers to how the image samples are transformed into spatial frequency components during the coding process. This use of the term “transform” should be distinguished from a geometric transform used to estimate scene changes in some interframe compression methods.

Interframe compression typically utilizes motion estimation and compensation to encode scene changes between frames. Motion estimation is a process for estimating the motion of image samples (e.g., pixels) between frames. Using motion estimation, the encoder attempts to match blocks of pixels in one frame with corresponding pixels in another frame. After the most similar block is found in a given search area, the change in position of the pixel locations of the corresponding pixels is approximated and represented as motion data, such as a motion vector. Motion compensation is a process for determining a predicted image and computing the error between the predicted image and the original image. Using motion compensation, the encoder applies the motion data to an image and computes a predicted image. The difference between the predicted image and the input image is called the error signal. Since the error signal is just an array of values representing the difference between image sample values, it can be compressed using the same texture coding method as used for intraframe coding of image samples.

Although differing in specific implementations, the MPEG-1, MPEG-2, and H.26X video compression standards are similar in a number of respects. The following description of the MPEG-2 video compression standard is generally applicable to the others.

MPEG-2 provides interframe compression and intraframe compression based upon square blocks or arrays of pixels in video images. A video image is divided into image sample blocks called macroblocks having dimensions of 16×16 pixels. In MPEG-2, a macroblock comprises four luminance blocks (each block is 8×8 samples of luminance (Y)) and two chrominance blocks (one 8×8 sample block each for Cb and Cr).

In MPEG-2, interframe coding is performed on macroblocks. An MPEG-2 encoder performs motion estimation and compensation to compute motion vectors and block error signals. For each block MN in an image frame N, a search is performed across the image of a next successive video frame N+1 or immediately preceding image frame N−1 (i.e., bi-directionally) to identify the most similar respective blocks M_(N+1) or M_(N−1). The location of the most similar block relative to the block MN is encoded with a motion vector (DX,DY). The motion vector is then used to compute a block of predicted sample values. These predicted sample values are compared with block MN to determine the block error signal. The error signal is compressed using a texture coding method such as discrete cosine transform (DCT) encoding.

Object-based video coding techniques have been proposed as an improvement to the conventional frame-based coding standards. In object-based coding, arbitrary shaped image features are separated from the frames in the video sequence using a method called “segmentation.” The video objects or “segments” are coded independently. Object-based coding can improve the compression rate because it increases the interframe correlation between video objects in successive frames. It is also advantageous for variety of applications that require access to and tracking of objects in a video sequence.

In the object-based video coding methods proposed for the MPEG-4 standard, the shape, motion and texture of video objects are coded independently. The shape of an object is represented by a binary or alpha mask that defines the boundary of the arbitrary shaped object in a video frame. The motion of an object is similar to the motion data of MPEG-2, except that it applies to an arbitrary-shaped image of the object that has been segmented from a rectangular frame. Motion estimation and compensation is performed on blocks of a “video object plane” rather than the entire frame. The video object plane is the name for the shaped image of an object in a single frame.

The texture of a video object is the image sample information in a video object plane that falls within the object's shape. Texture coding of an object's image samples and error signals is performed using similar texture coding methods as in frame-based coding. For example, a segmented image can be fitted into a bounding rectangle formed of macroblocks. The rectangular image formed by the bounding rectangle can be compressed just like a rectangular frame, except that transparent macroblocks need not be coded. Partially transparent blocks are coded after filling in the portions of the block that fall outside the object's shape boundary with sample values in a technique called “padding.”

In both frame-based and object-based video coding, the encoded bit stream typically includes many interframe-coded frames (P frames). Each of these P frames includes at least one motion vector per macroblock, and each motion vector includes X and Y components that coded independently. As such, motion vectors contribute a significant amount of data for each coded P frame. There is a need, therefore, for more efficient motion vector coding schemes.

SUMMARY OF THE INVENTION

The invention provides an improved method of coding motion vectors for video coding applications. One aspect of the invention is a method for jointly coding a motion vector with a single entropy code. This method is based on the discovery that the probability of the X and Y components of the motion vector are not totally independent. To exploit the correlation between the motion vector components, the method uses entropy coding to assign a single variable length code to a joint parameter representing the combined X and Y components of the motion vector. Motion vector component pairs that are more likely are assigned a shorter length code, while less likely component pairs are assigned a longer length code or are coded with an escape code followed by a code for each component. This approach can be used in a variety of video coding applications, including both object-based and frame based coding. In addition, joint entropy coding of motion vectors can be used in combination with spatial prediction to code motion vectors more efficiently.

For example, in one implementation, an encoder first computes a predictor for the motion vector, and then computes differential X and Y components from the X and Y components of the vector currently being processed and its predictor. A joint entropy coder then computes a single variable length code for a joint parameter representing both the X and Y differential components.

The decoder performs the inverse of the encoder operations to reconstruct the motion vector from the variable length code. In particular, it computes the joint parameter from the variable length code, and then reconstructs the motion vector from the differential components and the components of the predictor.

Additional features of the invention will become more apparent from the following detailed description and accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a video coder.

FIG. 2 is a block diagram of a video decoder.

FIG. 3 is a block diagram illustrating how an implementation of the invention jointly codes motion vector components for a macroblock with a single entropy code.

FIG. 4 is a diagram illustrating how a predictor for the motion vector of a current block is selected from motion vectors of neighboring macroblocks.

FIG. 5 is a diagram illustrating how a motion vector predictor is selected in cases where one or more neighboring macroblocks are outside the picture.

FIG. 6 is a block diagram illustrating how an implementation of the invention decodes a jointly coded motion vector.

FIG. 7 is a diagram of a computer system that serves as an operating environment for a software implementation of the invention.

DETAILED DESCRIPTION

Introduction

The first section below provides a description of a video encoder and decoder. Subsequent sections describe how to improve coding of motion vectors by exploiting the correlation between the X and Y components of the vectors.

This approach for jointly coding the X and Y components of a motion vector applies to both frame-based and object-based video coding. Both forms of video coding employ motion vectors to define the motion of a pixel or block of pixels from one frame to another. Typically, a motion vector is computed for regular sized blocks of pixels. In frame-based coding, the frame is divided into regular sized blocks. In object-based coding, each video object plane is divided into blocks. Since the object represented in a video object plane usually has a non-rectangular shape, object-based coders use the shape to determine which pixels in each block fall within the boundaries of the object. While frame-based and object-based coding differ in this respect, both approaches use motion vectors that define the motion of pixels in a block. Thus, the correlation between the X and Y components of motion vectors in both types of coders can be exploited to improve coding efficiency.

While the encoder and decoder described in the next section are object-based, they provide a sufficient basis for explaining how to implement the invention in both frame-based and object-based coding schemes.

Description of an Example Encoder and Decoder

FIG. 1 is a block diagram illustrating an implementation of an object-based video encoder. The input 30 to the encoder includes images representing the video objects in each frame, the shape of each video object and bounding rectangles. The shape information is available before the encoder codes texture or motion data. Frame-based coding differs in that the entire frame is coded without shape information, and the input 30 consists of a series of image frames.

The shape coding module 32 reads the definition of an object including its bounding rectangle and extends the bounding rectangle to integer multiples of macroblocks. The shape information for an object comprises a mask or “alpha plane.” The shape coding module 32 reads this mask and compresses it, using for example, a conventional chain coding method to encode the contour of the object.

Motion estimation module 34 reads an object including its bounding rectangle and a previously reconstructed image 36 and computes motion estimation data used to predict the motion of an object from one frame to another. The motion estimation module 34 searches for the most similar macroblock in the reconstructed image for each macroblock in the current image to compute a motion vector for each macroblock. The specific format of the motion vector from the motion estimation module 34 can vary depending on the motion estimation method used. In the implementation described below, there is a motion vector for each macroblock, which is consistent with current MPEG and H26X formats.

The motion compensation module 38 reads the motion vectors computed by the motion estimation module and the previously reconstructed image 36 and computes a predicted image for the current frame. Each pixel in the predicted image is constructed by using the motion vector for the macroblock that it resides in to find the corresponding pixel in the previously reconstructed image 36. The encoder then finds the difference between the image sample values in the input image block as specified in the input 30 and the corresponding sample values in the predicted image block as computed in the motion compensation module 38 to determine the error signal for the macroblock.

Texture coding module 40 compresses this error signal for inter-frame coded objects and compresses image sample values for the object from the input data stream for intra-frame coded objects. The feedback path 42 from the texture coding module 40 represents the error signal. The encoder uses the error signal blocks along with the predicted image blocks from the motion compensation module to compute the previously reconstructed image 36.

The texture coding module 40 codes intra-frame and error signal data for an object using any of a variety of still image compression techniques. Example compression techniques include DCT, wavelet, as well as other conventional image compression methods.

The bit stream of the compressed video sequence includes the shape, motion and texture coded information from the shape coding, motion estimation, and texture coding modules. Multiplexer 44 combines and formats this data into the proper syntax and outputs it to the buffer 46. As explained in more detail below, the encoder also includes a motion vector encoder that uses entropy coding to jointly code the x and y components of the motion vector for each macroblock. The motion vector encoder may be implemented as part of the motion estimation module 34 or as part of the data formatting functions in the multiplexer 44.

While the encoder can be implemented in hardware or software, it is most likely implemented in software. In a software implementation, the modules in the encoder represent software instructions stored in memory of a computer and executed in the processor, and the video data stored in memory. A software encoder can be stored and distributed on a variety of conventional computer readable media. In hardware implementations, the encoder modules are implemented in digital logic, preferably in an integrated circuit. Some of the encoder functions can be optimized in special-purpose digital logic devices in a computer peripheral to off-load the processing burden from a host computer.

FIG. 2 is a block diagram illustrating a decoder for an object-based video coding method. A demultiplexer 60 receives a bit stream representing a compressed video sequence and separates shapes, motion and texture encoded data on an object by object basis. The demultiplexer also includes a motion vector decoder that reconstructs the motion vector for each macroblock from a single variable length code.

Shape decoding module 64 decodes the shape or contour for the current object being processed. To accomplish this, it employs a shape decoder that implements the inverse of the shape encoding method used in the encoder of FIG. 1. The resulting shape data is a mask, such as a binary alpha plane or gray scale alpha plane representing the shape of the object.

The motion decoding module 66 decodes the motion information in the bit stream. The decoded motion information includes the motion vectors for each macroblock that are reconstructed from entropy codes in the incoming bitstream. The motion decoding module 66 provides this motion information to the motion compensation module 68, and the motion compensation module 68 uses the motion vectors to find predicted image samples in the previously reconstructed object data 70.

The texture decoding module 74 decodes error signals for inter-frame coded texture data and an array of color values for intra-frame texture data and passes this information to a module 72 for computing and accumulating the reconstructed image. For inter-frame coded objects, this module 72 applies the error signal data to the predicted image output from the motion compensation module to compute the reconstructed object for the current frame. For intra-frame coded objects the texture decoding module 74 decodes the image sample values for the object and places the reconstructed object in the reconstructed object module 72. Previously reconstructed objects are temporarily stored in object memory 70 and are used to construct the object for other frames.

Like the encoder, the decoder can be implemented in hardware, software or a combination of both. In software implementations, the modules in the decoder are software instructions stored in memory of a computer and executed by the processor, and video data stored in memory. A software decoder can be stored and distributed on a variety of conventional computer readable media. In hardware implementations, the decoder modules are implemented in digital logic, preferably in an integrated circuit. Some of the decoder functions can be optimized in special-purpose digital logic devices in a computer peripheral to off-load the processing burden from a host computer.

Improved Coding of Motion Vectors

The coding efficiency of motion vectors can be improved by exploiting the correlation between the X and Y components of a motion vector. Traditional coding methods code the X and Y components separately based on the premise that the probability distribution of the X and Y components are independent. We have discovered that the X and Y components are not totally independent, but instead, have a correlation.

To take advantage of this correlation, an implementation of the invention assigns a single entropy code to the joint X and Y components of a motion vector. Before coding, sample video data for a target bit rate and content scenario is used to generate a codebook. This codebook assigns a single variable length code to pairs of X and Y components based on their frequency of occurrence. More frequent, and therefore statistically more probable pairs, are assigned shorter length codes, while less frequent pairs are assigned longer length codes. A statistical analysis program computes the probability of each of the joint X and Y components by extracting the motion vector data generated from an encoder for several example video sequences that have the desired type of content. The program creates a probability distribution for pairs of motion vectors (namely, differential motion vectors) and then assigns codes to a subset of the motion vectors that are most probable.

To limit the size of the codebook, low probability pairs need not be assigned a code. Instead, these pairs can be coded by using an escape code to indicate that the motion vector components follow in fix length bit fields. Pairs are excluded from the codebook based on where they fall in the probability distribution.

While not required, the coding of motion vectors can be improved by using a differential coding process that takes advantage of the spatial dependency of motion vectors. In particular, a motion vector for a small block of pixels is likely to point in a similar direction as the motion vector for a neighboring block, especially if both the current block and its neighbor are in a region of the frame having nearly uniform motion. One way to take advantage of this spatial dependency is to code the difference between a motion vector for the current block and the motion vector for a neighboring block, called the predictor. The implementation uses a form of spatial prediction to encode the X and Y components before assigning a joint entropy code.

FIG. 3 is a block diagram illustrating how our implementation encodes motion vectors. The features shown in FIG. 3 are implemented in the encoder and operate on the motion vectors computed in the motion estimation block 34. First, the motion estimation block computes a motion vector for each macroblock in the frame. When a frame consists of more than one video object plane, the motion estimation block computes motion vectors for the macroblocks of each video object plane.

The encoder begins coding the motion vector for each macroblock by computing a predictor for the current motion vector. The implementation shown in FIG. 3 selects a predictor from among neighboring macroblocks. FIG. 4 shows an example of the positioning of the candidates for the predictor relative to the current macroblock for which the motion vector is being encoded. In this example, the candidate macroblocks include the ones to the left 400, above 402, and above-right 404 relative to the current macroblock 406. The motion vectors for the candidate macroblocks are referred to as MV1, MV2, and MV3, respectively.

As shown in FIG. 3, the encoder computes the predictor separately for the X and Y components of the current macroblock. In particular, the motion vector predictors 300, 302 compute the median of the X and Y components for the candidate macroblocks. The median of these three values is chosen as the predictor for the X and Y components. The precise method of computing the predictor is not critical to the invention and other ways of selecting a predictor are possible. One alternative is to select a neighboring block located in the direction of the lowest gradient of the neighboring motion vectors. Another alternative is to compute an average of motion vectors of neighboring blocks.

Once the motion vector predictor selects the predictor, the encoder computes differential motion vector components. For each X and Y component, the encoder computes the difference between the component of the current motion vector and the corresponding component of the predictor. As reflected by subtractor units 304, 306 in FIG. 3, the X component of the predictor is subtracted from the X component of the current vector MVx, and the Y component of the predictor is subtracted from the Y component of the current vector MVy.

The resulting differential X and Y components (MVDx and MVDy) are then formed into a joint parameter that is coded with a single variable length code, or an escape code followed by fixed code word for each differential component. The implementation uses a joint Huffman coding table that is trained for a target bit rate and video content. The joint entropy coder 308 looks up the joint parameter in the table to find a corresponding variable length code. If the coder finds a match in the table, it codes the joint parameter with a single variable length code. Otherwise, it codes an escape code followed by a fixed length code word for each component.

The entropy codes 310 shown in FIG. 3 refer to the Huffman coding table. An example of a Huffman coding table trained for low bit rate, talking head applications is set forth at the end of this section in Table 1. Following Table 1, Table 2 is an example of a Huffman table trained for more general video applications. While our implementation uses Huffman coding tables, the entropy codes can be computed using other forms of entropy coding such as arithmetic coding.

Since the predictor is selected from motion vectors of neighboring blocks of pixels, the encoder applies special rules to address the situation where one or more neighboring blocks are outside the picture. FIG. 5 illustrates cases where a neighboring block is outside the picture and shows the motion vectors that are used to predict the motion vector in the current macroblock.

If one neighboring block is outside the picture (e.g., block 500 in FIG. 5), a zero motion vector (0,0) is used in its place. The predictor of the current macroblock 506 is computed as the median of the zero motion vector, and motion vectors MV2 and MV3 for the other two neighboring macroblocks 502, 504. As another example, the configuration on the far right of FIG. 5 shows the case where the above-right macroblock 524 is out of the picture. In this case, MV1 and MV2 for the other two macroblocks 520, 522 inside the picture are used along with the zero motion vector for the third macroblock 524 to predict the motion vector for the current macroblock 526.

If two candidate macroblocks 512, 514 are out of the picture (as shown in the middle diagram of FIG. 5), then the motion vector for the third neighboring macroblock 510 is selected as the predictor for the current macroblock 516.

FIG. 6 is a diagram illustrating an implementation of a decoder for decoding a single variable length code representing joint motion vector components into X and Y motion vector components. The joint entropy decoder 600 reads the variable length code as input and finds the corresponding differential X and Y components in the entropy codes 602. In the current implementation, the entry codes are in the form of a Huffman table (e.g., tables 1 or 2 listed below). As noted above, the encoder can also use an alternative entropy coding scheme, in which case, the decoder would have the appropriate codebook to correspond with the codebook used in the encoder.

In some cases, the motion vector may be coded with an escape code followed by two fixed length codes representing the differential motion vector components. In this case, the joint entropy decoder 600 recognizes the escape code and interprets the following data as differential motion vectors instead of a variable length code. It then passes the differential X and Y components to the next stage.

Next, the decoder forms the motion vector from the differential motion vector components MVDx, MVDy and the X and Y components of the predictor. In particular the decoder adds each differential motion vector component MVDx, MVDy and the X and Y components of the predictor (see adders 604, 606, FIG. 6). The decoder computes the predictor components in the same way as the encoder. In particular, it has a motion vector predictor that computes the predictor of the motion vectors previously decoded for the three neighboring macroblocks (MVx1, MVy), (MVx2, MVy2) and (MVx3, MVy3). In the implementation, the motion vector predictor blocks 608, and 610 represent the computation of the median of the X and Y components, respectively, of the neighboring macroblocks. As noted above, other ways of computing the predictor are possible. Regardless of the specific form of prediction, the decoder performs inverse prediction according to the prediction scheme used in the encoder.

Once the motion vector for the current macroblock (MVx, MVy) is reconstructed, it is stored and used to decode the motion vector for neighboring macroblocks according to the prediction scheme.

The following tables provide examples of Huffman coding tables trained for talking head video (Table 1) and more general video content (Table 2).

TABLE 1 XY Joint VLC Motion Vector Table for Talking Head Video Index Mv_(—)x Mv_(—)y Number of bits Code 0 0 0 1 1 1 0 −0.5 4 0011 2 −0.5 0 4 0101 3 0 0.5 4 0111 4 0.5 0 5 00010 5 −0.5 −0.5 5 01000 6 0.5 −0.5 5 01101 7 −0.5 0.5 6 000000 8 0.5 0.5 6 000001 9 0 1 6 011001 10 1 0 7 0000101 11 0 −1 7 0001111 12 −1 0 7 0010110 13 0 1.5 8 00001001 14 −0.5 1 8 00001101 15 1 −0.5 8 00001110 16 1.5 0 8 00011011 17 0 −1.5 8 00011101 18 1 0.5 8 00100001 19 0.5 −1 8 00100110 20 −1.5 0 8 00101000 21 0.5 1 8 00101010 22 −1 0.5 8 00101110 23 −1 −0.5 8 01001100 24 −0.5 −1 8 01001101 25 −0.5 1.5 9 000010001 26 1.5 −0.5 9 000110000 27 −1.5 −0.5 9 000110001 28 0.5 −1.5 9 000110011 29 1.5 0.5 9 000110101 30 0.5 1.5 9 001000000 31 1 −1 9 001001010 32 −0.5 −1.5 9 001001011 33 −1.5 0.5 9 001010010 34 −1 1 9 001011110 35 1 1 9 010010010 36 −1 −1 9 011000000 37 2 0 10 0000110011 38 −2 0 10 0000111111 39 0 2 10 0001101000 40 1 −1.5 10 0001110000 41 2.5 0 10 0001110001 42 −1 1.5 10 0010010000 43 −2.5 0 10 0010011100 44 0 −2 10 0010011101 45 −3.5 0 10 0010011111 46 3.5 0 10 0010101100 47 0 −2.5 10 0010101101 48 1 1.5 10 0100100010 49 0 2.5 10 0100100011 50 1.5 1 10 0100101000 51 1.5 −1.5 10 0100111001 52 1.5 −1 10 0100111011 53 −0.5 2 10 0110000011 54 1.5 1.5 10 0110000101 55 −1.5 1 10 0110000110 56 0 −3.5 10 0110001000 57 −1.5 −1 10 0110001001 58 −1 −1.5 10 0110001111 59 −1.5 1.5 11 00001000001 60 2.5 0.5 11 00001100001 61 −2.5 −0.5 11 00001100010 62 2 −0.5 11 00001111101 63 3 0 11 00011001000 64 2.5 −0.5 11 00011010011 65 0.5 −2 11 00011100100 66 0 3.5 11 00011100111 67 −0.5 −2 11 00100000100 68 −1.5 −1.5 11 00100000101 69 −0.5 2.5 11 00100100100 70 −2 −0.5 11 00100100101 71 2 0.5 11 00100111100 72 0.5 −2.5 11 00100111101 73 −1 2 11 00101001111 74 1 −2 11 00101111100 75 0.5 2 11 00101111101 76 0.5 2.5 11 00101111110 77 −2 0.5 11 01001000000 78 −2.5 0.5 11 01001001100 79 −3.5 −0.5 11 01001001111 80 −0.5 −2.5 11 01001010110 81 −3 0 11 01001011100 82 3.5 −0.5 11 01001110001 83 0 3 11 01001110100 84 0 −3 11 01100010110 85 −0.5 −3.5 11 01100010111 86 0.5 −3.5 11 01100011001 87 3.5 0.5 11 01100011100 88 −0.5 3.5 12 000010000100 89 3 −0.5 12 000010000101 90 −2 1 12 000010000111 91 2 −1 12 000011001000 92 −5.5 0 12 000011001001 93 −4.5 0 12 000011001010 94 5.5 0 12 000011001011 95 2 1 12 000011110001 96 1 2 12 000011110010 97 4.5 0 12 000011111000 98 −1 −2 12 000110010101 99 −3.5 0.5 12 000110100101 100 −2 −1 12 000111001101 101 −0.5 3 12 001000001101 102 −1 2.5 12 001001000111 103 1 −2.5 12 001001001101 104 3 0.5 12 001010011101 105 1.5 −2 12 001010111000 106 14.5 0 12 001010111110 107 1 2.5 12 010010011010 108 −2 1.5 12 010010011100 109 −1 3 12 010010100111 110 2.5 −1.5 12 010010101000 111 2.5 1 12 010010101011 112 1.5 −2.5 12 010010101110 113 −2.5 −1.5 12 010010101111 114 2 −1.5 12 010010110101 115 −14.5 0 12 010010110110 116 13.5 0 12 010010110111 117 3 1 12 010010111100 118 2.5 1.5 12 010010111110 119 0 −14.5 12 010010111111 120 −0.5 −3 12 010011100001 121 −1.5 2 12 010011111100 122 −3 −0.5 12 010011111101 123 0.5 3 12 010011111111 124 2.5 −1 12 011000001000 125 0.5 −3 12 011000001001 126 −2.5 1.5 12 011000001010 127 −2.5 1 12 011000001011 128 1.5 2.5 12 011000010000 129 1 −3 12 011000011100 130 1 −3.5 12 011000011110 131 4 0 12 011000011111 132 5 0 12 011000101010 133 0.5 3.5 12 011000101011 134 0 −4.5 12 011000110000 135 −1.5 2.5 12 011000110111 136 −14 0 12 011000111010 137 −13.5 0 13 0000100000000 138 −2 −1.5 13 0000100000001 139 −4 0 13 0000100001100 140 −3.5 −1.5 13 0000110000011 141 1.5 2 13 0000110001110 142 3.5 −1.5 13 0000111100000 143 3 −1 13 0000111100001 144 0 4.5 13 0000111101111 145 −4.5 −0.5 13 0000111110010 146 −2.5 −1 13 0000111110011 147 0 −5.5 13 0001100100101 148 −1 3.5 13 0001100100110 149 1.5 −3.5 13 0001100100111 150 −3 1 13 0001100101000 151 1 3 13 0001100101001 152 14 0 13 0001101001001 153 2 1.5 13 0001110010100 154 −1.5 3.5 13 0001110010101 155 −5 0 13 0001110011001 156 −3 0.5 13 0010000011000 157 4.5 0.5 13 0010010011000 158 −12.5 0 13 0010010011001 159 −1 −2.5 13 0010010011100 160 3 −1.5 13 0010010011110 161 −1 −3.5 13 0010010011111 162 2 −2 13 0010100110000 163 −1.5 −2.5 13 0010100110010 164 −1 −3 13 0010101110011 165 4.5 −0.5 13 0010101110100 166 −3 −1 13 0010101110101 167 −3.5 1.5 13 0010101111011 168 0 −4 13 0010101111111 169 1 −4 13 0010111111100 170 −4 −0.5 13 0100100001111 171 3.5 1 13 0100100110110 172 −15.5 0 13 0100101001010 173 −3.5 −1 13 0100101001011 174 3.5 1.5 13 0100101001100 175 0 4 13 0100101010010 176 −2 −2 13 0100101010011 177 −1.5 3 13 0100101010100 178 0 −13.5 13 0100101010101 179 3 1.5 13 0100101101000 180 −3 −1.5 13 0100101101001 181 2 2 13 0100101110101 182 −2 2 13 0100101110110 183 15.5 0 13 0100101110111 184 −2 3 13 0100101111011 185 3.5 −1 13 0100111000000 186 −4.5 0.5 13 0100111000001 187 −5.5 −0.5 13 0100111110110 188 −3 1.5 13 0100111110111 189 1.5 −3 13 0100111111100 190 −0.5 −4.5 13 0100111111101 191 1.5 3 13 0110000100110 192 12.5 0 13 0110000100111 193 −0.5 4.5 13 0110000111010 194 −1.5 −2 13 0110001010000 195 −1.5 −3.5 13 0110001010001 196 −2 2.5 13 0110001010010 197 −1 4 13 0110001010011 198 −2.5 2.5 13 0110001110110 199 1.5 3.5 14 00001000000100 200 −15 0 14 00001000000101 201 3 2 14 00001000000110 202 4 0.5 14 00001100000001 203 1 3.5 14 00001100000010 204 2.5 −3.5 14 00001100000011 205 −1.5 −3 14 00001100000100 206 3 −2 14 00001100000101 207 5.5 −0.5 14 00001100011000 208 −3 −2 14 00001100011001 209 0 5 14 00001100011010 210 0.5 −4.5 14 00001100011011 211 5 −0.5 14 00001100011110 212 −4 0.5 14 00001111011010 213 4 −0.5 14 00001111011011 214 −2 3.5 14 00001111011100 215 0 −15.5 14 00001111011101 216 0 13.5 14 00011001001000 217 0 −5 14 00011001001001 218 2 −2.5 14 00011001011110 219 0 −14 14 00011001011111 220 5.5 0.5 14 00011010010000 221 −3.5 1 14 00011010010001 222 −5.5 0.5 14 00011100101101 223 −0.5 −4 14 00011100101110 224 −1 4.5 14 00011100101111 225 −0.5 −14.5 14 00011100110000 226 4.5 1.5 14 00011100110001 227 −1.5 4.5 14 00100100011010 228 0.5 4.5 14 00100100011011 229 2.5 −2 14 00100100111010 230 −3 2 14 00100100111011 231 2.5 2 14 00101001100010 232 −2.5 −2 14 00101001110001 233 13.5 0.5 14 00101001110010 234 −4.5 1.5 14 00101001110011 235 0.5 −5.5 14 00101011100100 236 1.5 −4.5 14 00101011100101 237 −0.5 −5.5 14 00101011101101 238 −0.5 −5 14 00101011101110 239 2.5 2.5 14 00101011101111 240 3 −2.5 14 00101011110000 241 3.5 −2.5 14 00101011110001 242 0 5.5 14 00101011110010 243 −4.5 −1.5 14 00101011110011 244 0 14 14 00101011110100 245 −2.5 3.5 14 00101011110101 246 2.5 −2.5 14 00101011111100 247 2 −3.5 14 01001000010101 248 −0.5 13.5 14 01001000010110 249 4 1 14 01001000010111 250 −3.5 −2.5 14 01001000011000 251 −2.5 −2.5 14 01001000011001 252 3 −3 14 01001000011010 253 −0.5 4 14 01001000011011 254 2 2.5 14 01001000011100 255 −2 −2.5 14 01001000011101 256 −0.5 14.5 14 01001001101111 257 2 −3 14 01001001110100 258 −3.5 3.5 14 01001001110101 259 6.5 0.5 14 01001001110110 260 −14.5 −0.5 14 01001001110111 261 1 −5 14 01001010010000 262 3 2.5 14 01001010010001 263 3.5 −3.5 14 01001010010010 264 4 −1 14 01001010010011 265 3 −3.5 14 01001010011010 266 −1 −4 14 01001011001010 267 0 14.5 14 01001011001011 268 −6.5 −0.5 14 01001011001100 269 −4 1 14 01001011001101 270 −3.5 −3.5 14 01001011001110 271 −3 3 14 01001011001111 272 6.5 0 14 01001011101000 273 −6 0 14 01001011101001 274 −4 −1 14 01001011110100 275 0.5 −14.5 14 01001011110101 276 0.5 14.5 14 01001111011101 277 −0.5 5.5 14 01001111011110 278 4.5 −1.5 14 01001111011111 279 1 −4.5 14 01001111100000 280 3.5 −2 14 01001111100001 281 7.5 0 14 01001111100010 282 4 −2 14 01001111100011 283 13 0 14 01001111100100 284 13.5 −0.5 14 01001111100101 285 4.5 1 14 01001111100110 286 0.5 −13.5 14 01001111100111 287 −14.5 0.5 14 01001111101000 288 −7.5 0 14 01001111101001 289 14.5 0.5 14 01001111101010 290 5 0.5 14 01001111101011 291 −1 5 14 01100001000100 292 −3 2.5 14 01100001000101 293 −1.5 −4.5 14 01100001000110 294 2 3 14 01100001000111 295 14.5 −0.5 14 01100001001000 296 0.5 4 14 01100001001001 297 2.5 −3 14 01100001001010 298 15 0 14 01100001001011 299 −2 −3 14 01100001110110 300 −3.5 2.5 14 01100011011001 301 3 3 14 01100011011010 302 −3.5 2 14 01100011011011 303 3 −4 14 01100011101110 304 −7.5 −1.5 14 01100011101111 305 −4.5 −1 15 000010000001110 306 1 −6 15 000010000001111 307 0.5 −5 15 000010000110100 308 −5.5 −1.5 15 000010000110101 309 0.5 −4 15 000010000110110 310 8.5 0 15 000010000110111 311 −2.5 4.5 15 000011000000000 312 0 −15 15 000011000000001 313 −4.5 1 15 000011110101001 314 −2.5 −3.5 15 000011110101010 315 −5 0.5 15 000011110101011 316 −4 −1.5 15 000011110101100 317 −5 −0.5 15 000011110101101 318 3.5 3.5 15 000011110101110 319 5.5 1.5 15 000011110101111 320 −2.5 2 15 000011110110000 321 2.5 −4 15 000011110110001 322 −13 0 15 000011110110010 323 5 −1 15 000011110110011 324 7.5 0.5 15 000110010110000 325 −3 −2.5 15 000110010110001 326 −1 6 15 000110010110010 327 −0.5 14 15 000110010110011 328 4.5 −1 15 000110010110100 329 3.5 2 15 000110010110101 330 0.5 −6.5 15 000110010110110 331 −5 1 15 000110010110111 332 6.5 −0.5 15 000110010111000 333 2 −4 15 000110010111001 334 0 −8 15 000110010111010 335 6.5 1.5 15 000110010111011 336 −6.5 0 15 000111001011000 337 −5 3 15 001001000100100 338 −1 −5.5 15 001001000100101 339 −13.5 0.5 15 001001000100110 340 −13.5 −0.5 15 001001000100111 341 −7.5 −0.5 15 001001000101000 342 −1.5 −5.5 15 001001000101001 343 −5 1.5 15 001001000101010 344 −0.5 −13.5 15 001001000101011 345 −0.5 −7.5 15 001001000101100 346 5.5 −1.5 15 001001000101101 347 2.5 3 15 001001000101110 348 −2.5 3 15 001001000101111 349 0 −7 15 001001000110000 350 0 13 15 001001000110001 351 0 −6.5 15 001001000110010 352 0.5 5.5 15 001001000110011 353 1 4.5 15 001010011000110 354 5.5 −1 15 001010011000111 355 1.5 4.5 15 001010011001100 356 −1.5 5.5 15 001010011001101 357 −3 3.5 15 001010011001110 358 −5 −1.5 15 001010011001111 359 0 −12.5 15 001010011010000 360 −6.5 −1.5 15 001010011010001 361 0 −7.5 15 001010011010010 362 −3.5 −2 15 001010011010011 363 −0.5 −6.5 15 001010011010100 364 4.5 −2 15 001010011010101 365 8.5 −0.5 15 001010011010110 366 −2 −3.5 15 001010011010111 367 1 −6.5 15 001010011011000 368 −2 4 15 001010011011001 369 3.5 −3 15 001010011011010 370 1 −5.5 15 001010011011011 371 −6.5 0.5 15 001010011011100 372 2.5 3.5 15 001010011011101 373 3 −4.5 15 001010011011110 374 −1.5 4 15 001010011011111 375 −5.5 −1 15 001010011100000 376 2 3.5 15 001010011100001 377 5 1 15 001010111011000 378 −4 1.5 15 010010000011011 379 8 0 15 010010000011100 380 −8 0 15 010010000011101 381 −2 −4 15 010010000011110 382 8.5 0.5 15 010010000011111 383 −5 −1 15 010010000100000 384 1 4 15 010010000100001 385 −0.5 7.5 15 010010000100010 386 3 3.5 15 010010000100011 387 3.5 2.5 15 010010000100100 388 6 0 15 010010000100101 389 −10.5 0.5 15 010010000100110 390 1.5 −4 15 010010000100111 391 −1 −4.5 15 010010000101000 392 0.5 6.5 15 010010000101001 393 0.5 7.5 15 010010011011100 394 −4.5 −2.5 15 010010011011101 395 −2 −4.5 15 010010100110110 396 0.5 5 15 010010100110111 397 7 0 15 010010110000000 398 −8.5 0 15 010010110000001 399 −9.5 0.5 15 010010110000010 400 −4 2 15 010010110000011 401 4.5 2.5 15 010010110000100 402 −4 2.5 15 010010110000101 403 1 −7.5 15 010010110000110 404 1 −7 15 010010110000111 405 −1 −5 15 010010110001000 406 −3 4 15 010010110001001 407 −4 3 15 010010110001010 408 −9 0 15 010010110001011 409 14 −0.5 15 010010110001100 410 −5.5 1.5 15 010010110001101 411 −1.5 −4 15 010010110001110 412 3.5 −7.5 15 010010110001111 413 −4.5 −3.5 15 010010110010000 414 1.5 −7.5 15 010010110010001 415 2.5 −4.5 15 010010110010010 416 15.5 0.5 15 010010110010011 417 6.5 1 15 010011110100010 418 0.5 9.5 15 010011110100011 419 1 5 15 010011110100100 420 7.5 −0.5 15 010011110100101 421 4.5 2 15 010011110100110 422 −5 2 15 010011110100111 423 5 −1.5 15 010011110101000 424 1.5 −5.5 15 010011110101001 425 1.5 −5 15 010011110101010 426 −4.5 2.5 15 010011110101011 427 0 6 15 010011110101100 428 1.5 5.5 15 010011110101101 429 5.5 −3.5 15 010011110101110 430 0 7.5 15 010011110101111 431 −12.5 0.5 15 010011110110000 432 −0.5 6.5 15 010011110110001 433 4.5 −2.5 15 010011110110010 434 −6 −0.5 15 010011110110011 435 −0.5 13 15 010011110110100 436 −8 −0.5 15 010011110110101 437 −9.5 0 15 010011110110110 438 15.5 −0.5 15 010011110110111 439 −3.5 3 15 010011110111000 440 −1 5.5 15 010011110111001 441 0 −6 15 011000011101110 442 1.5 7.5 15 011000011101111 443 −1 6.5 15 011000110001000 444 −1 11 15 011000110001001 445 −0.5 −15.5 15 011000110001010 446 5 −3 15 011000110001011 447 7.5 1 15 011000110001100 448 3.5 3 15 011000110001101 449 3 −9 15 011000110001110 450 4 −5 15 011000110001111 451 4 −4 15 011000110100000 452 9.5 0.5 15 011000110100001 453 11.5 1 15 011000110100010 454 12 0 15 011000110100011 455 −7 0 15 011000110100100 456 −5.5 2.5 15 011000110100101 457 3.5 −5.5 15 011000110100110 458 3.5 −4.5 15 011000110100111 459 0.5 8.5 15 011000110101000 460 −7.5 1.5 15 011000110101001 461 4.5 −4.5 15 011000110101010 462 −4.5 −2 15 011000110101011 463 −4 3.5 15 011000110101100 464 5.5 3.5 15 011000110101101 465 −3.5 −4.5 15 011000110101110 466 −0.5 11.5 15 011000110101111 467 −6 0.5 15 011000110110000 468 −6.5 −1 15 011000110110001 469 6.5 −1 16 0000110001111100 470 −15.5 15.5 16 0000110001111101 471 1 −8 16 0000110001111110 472 −0.5 5 16 0000110001111111 473 −5 −2 16 0000111100110000 474 1.5 −9.5 16 0000111100110001 475 −8.5 0.5 16 0000111100110010 476 7 0.5 16 0000111100110011 477 7 1.5 16 0000111100110100 478 1.5 −6.5 16 0000111100110101 479 −0.5 7 16 0000111100110110 480 −2 5.5 16 0000111100110111 481 −1.5 −7.5 16 0000111100111000 482 −1.5 −6.5 16 0000111100111001 483 −4.5 2 16 0000111100111010 484 4.5 3.5 16 0000111100111011 485 −2.5 −4 16 0000111100111100 486 −9 −0.5 16 0000111100111101 487 10.5 0 16 0000111100111110 488 10.5 0.5 16 0000111100111111 489 −2.5 −3 16 0000111101000000 490 −4 −2 16 0000111101000001 491 0 15 16 0000111101000010 492 12.5 0.5 16 0000111101000011 493 0 15.5 16 0000111101000100 494 −7.5 0.5 16 0000111101000101 495 5 3.5 16 0000111101000110 496 2.5 −6.5 16 0000111101000111 497 −1.5 8.5 16 0000111101001000 498 0.5 −7.5 16 0000111101001001 499 −15.5 −0.5 16 0000111101001010 500 −3.5 5.5 16 0000111101001011 501 0 −9.5 16 0000111101001100 502 0 −8.5 16 0000111101001101 503 15.5 −1.5 16 0000111101001110 504 −3 −3.5 16 0000111101001111 505 4 1.5 16 0000111101010000 506 6 0.5 16 0000111101010001 507 2 −4.5 16 0001110010110010 508 −0.5 8.5 16 0001110010110011 509 3.5 4.5 16 0010000011001000 510 −6 −2 16 0010000011001001 511 −6 −1.5 16 0010000011001010 512 6 1 16 0010000011001011 513 −4.5 3 16 0010000011001100 514 0.5 −12.5 16 0010000011001101 515 1 14.5 16 0010000011001110 516 1.5 −10.5 16 0010000011001111 517 0.5 9 16 0010000011100000 518 0.5 −9.5 16 0010000011100001 519 −2 4.5 16 0010000011100010 520 4.5 −6.5 16 0010000011100011 521 −4.5 7.5 16 0010000011100100 522 4.5 −3.5 16 0010000011100101 523 4.5 −3 16 0010000011100110 524 −1.5 −8.5 16 0010000011100111 525 −3.5 5 16 0010000011101000 526 −3 4.5 16 0010000011101001 527 8.5 −1.5 16 0010000011101010 528 −1.5 6.5 16 0010000011101011 529 −4 −2.5 16 0010000011101100 530 2.5 −7.5 16 0010000011101101 531 8.5 1.5 16 0010000011101110 532 9 0 16 0010000011101111 533 9.5 −1.5 16 0010000011110000 534 9.5 0 16 0010000011110001 535 −3 −4 16 0010000011110010 536 3.5 −9.5 16 0010000011110011 537 −3.5 −3 16 0010000011110100 538 −3 −3 16 0010000011110101 539 −8.5 −0.5 16 0010000011110110 540 3.5 −4 16 0010000011110111 541 −7 0.5 16 0010000011111000 542 5 −2 16 0010000011111001 543 −7.5 −1 16 0010000011111010 544 −14 −0.5 16 0010000011111011 545 −0.5 −10.5 16 0010000011111100 546 0 6.5 16 0010000011111101 547 0 7 16 0010000011111110 548 14 0.5 16 0010000011111111 549 −15.5 0.5 16 0010010001000000 550 5 1.5 16 0010010001000001 551 0 12.5 16 0010010001000010 552 −16 0 16 0010010001000011 553 −10 0 16 0010010001000100 554 −6.5 1.5 16 0010010001000101 555 1.5 6.5 16 0010010001000110 556 −5.5 1 16 0010010001000111 557 4.5 −10.5 16 0010101110110010 558 −7.5 2.5 16 0010101110110011 559 −3 5 16 0010101111110100 560 −6 3.5 16 0010101111110101 561 6.5 2.5 16 0010101111110110 562 7 −0.5 16 0010101111110111 563 0 8.5 16 0010111111101000 564 2.5 −5.5 16 0010111111101001 565 −5 −2.5 16 0010111111101010 566 7.5 −1.5 16 0010111111101011 567 −1.5 7.5 16 0010111111101100 568 −0.5 10.5 16 0010111111101101 569 −2.5 4 16 0010111111101110 570 −1.5 9.5 16 0010111111101111 571 −1 −8 16 0010111111110000 572 −5.5 −3 16 0010111111110001 573 0.5 −15.5 16 0010111111110010 574 1.5 4 16 0010111111110011 575 −7 −1 16 0010111111110100 576 −3.5 4.5 16 0010111111110101 577 0.5 6 16 0010111111110110 578 9 1 16 0010111111110111 579 9.5 −3.5 16 0010111111111000 580 5 −2.5 16 0010111111111001 581 −15 −0.5 16 0010111111111010 582 −8.5 1.5 16 0010111111111011 583 9.5 1.5 16 0010111111111100 584 10.5 −0.5 16 0010111111111101 585 0.5 −8.5 16 0010111111111110 586 −3.5 8.5 16 0010111111111111 587 −1.5 −15.5 16 0100100000100000 588 11.5 1.5 16 0100100000100001 589 2.5 4 16 0100100000100010 590 3 −13.5 16 0100100000100011 591 0.5 13 16 0100100000100100 592 3 −5.5 16 0100100000100101 593 13.5 −1.5 16 0100100000100110 594 3 −5 16 0100100000100111 595 0.5 13.5 16 0100100000101000 596 3.5 6.5 16 0100100000101001 597 −9.5 −0.5 16 0100100000101010 598 0 −11.5 16 0100100000101011 599 4 −3 16 0100100000101100 600 14.5 −11.5 16 0100100000101101 601 14.5 −1.5 16 0100100000101110 602 0 −10.5 16 0100100000101111 603 −11.5 0 16 0100100000110000 604 6 −1 16 0100100000110001 605 −14.5 −14.5 16 0100100000110010 606 −0.5 −9.5 16 0100100000110011 607 −1.5 −6 16 0100100000110100 608 −3.5 −7 16 0100100000110101 609 −0.5 −6 16 0100111010100000 610 −2.5 −10.5 16 0100111010100001 611 −4.5 −14.5 16 0100111010100010 612 −11.5 −1.5 16 0100111010100011 613 −3.5 4 16 0100111010100100 614 −11.5 −0.5 16 0100111010100101 615 −1.5 10.5 16 0100111010100110 616 −6 −1 16 0100111010100111 617 −1 −7.5 16 0100111010101000 618 −1 −6 16 0100111010101001 619 5 2.5 16 0100111010101010 620 −7 −0.5 16 0100111010101011 621 −2 5 16 0100111010101100 622 −3.5 7.5 16 0100111010101101 623 −2 7.5 16 0100111010101110 624 −2 11 16 0100111010101111 625 −5.5 3 16 0100111010110000 626 −1.5 −11.5 16 0100111010110001 627 5.5 1 16 0100111010110010 628 −1.5 −9.5 16 0100111010110011 629 5.5 2.5 16 0100111010110100 630 −3 −5.5 16 0100111010110101 631 6 −3.5 16 0100111010110110 632 6 −2.5 16 0100111010110111 633 −5.5 5.5 16 0100111010111000 634 3 5 16 0100111010111001 635 −5.5 6.5 16 0100111010111010 636 −4 4 16 0100111010111011 637 6.5 −3.5 16 0100111010111100 638 6.5 −2.5 16 0100111010111101 639 1.5 7 16 0100111010111110 640 3.5 −5 16 0100111010111111 641 −5 −3.5 16 0100111100000000 642 1.5 10.5 16 0100111100000001 643 2 −6 16 0100111100000010 644 1 −15 16 0100111100000011 645 1 −9 16 0100111100000100 646 6.5 3.5 16 0100111100000101 647 1 −8.5 16 0100111100000110 648 −1.5 −5 16 0100111100000111 649 −0.5 6 16 0100111100001000 650 7 1 16 0100111100001001 651 −3.5 −5.5 16 0100111100001010 652 7 3 16 0100111100001011 653 −8 0.5 16 0100111100001100 654 −7.5 −2.5 16 0100111100001101 655 −0.5 8 16 0100111100001110 656 −6 1 16 0100111100001111 657 0 10 16 0100111100010000 658 7.5 1.5 16 0100111100010001 659 7.5 7.5 16 0100111100010010 660 7.5 8.5 16 0100111100010011 661 0 11 16 0100111100010100 662 8.5 −15 16 0100111100010101 663 8.5 −9.5 16 0100111100010110 664 8.5 −4.5 16 0100111100010111 665 −0.5 10 16 0100111100011000 666 −15.5 −1.5 16 0100111100011001 667 −2.5 6.5 16 0100111100011010 668 −2 −5 16 0100111100011011 669 3.5 8.5 16 0100111100011100 670 3.5 11 16 0100111100011101 671 −5.5 −5.5 16 0100111100011110 672 2 4 16 0100111100011111 673 −4.5 5 16 0100111100100000 674 9.5 −0.5 16 0100111100100001 675 −15 −1 16 0100111100100010 676 4 −1.5 16 0100111100100011 677 9.5 1 16 0100111100100100 678 0 −16 16 0100111100100101 679 10.5 −3.5 16 0100111100100110 680 −4 −4.5 16 0100111100100111 681 −1 9.5 16 0100111100101000 682 −4 −4 16 0100111100101001 683 −1 13.5 16 0100111100101010 684 −5.5 −2 16 0100111100101011 685 4 3 16 0100111100101100 686 12.5 −1.5 16 0100111100101101 687 12.5 −0.5 16 0100111100101110 688 −0.5 −15 16 0100111100101111 689 4.5 −9.5 16 0100111100110000 690 13 −0.5 16 0100111100110001 691 0 −12 16 0100111100110010 692 −10 −0.5 16 0100111100110011 693 −14 0.5 16 0100111100110100 694 0 −10 16 0100111100110101 695 1 6.5 16 0100111100110110 696 13.5 4.5 16 0100111100110111 697 −0.5 −12.5 16 0100111100111000 698 0 −9 16 0100111100111001 699 −9.5 −1 16 0100111100111010 700 −11.5 −3.5 16 0100111100111011 701 1.5 −7 16 0100111100111100 702 −3 5.5 16 0100111100111101 703 1.5 −6 16 0100111100111110 704 2.5 5.5 16 0100111100111111 705 14.5 1.5 16 0100111101000000 706 2.5 6 16 0100111101000001 707 15.5 −15.5 16 0100111101000010 708 −3 8.5 16 0100111101000011 709 ESC ESC 7 0010001 @

TABLE 2 XY Joint VLC Motion Vector Table for General Video Index Mv_(—)x Mv_(—)y Number of bits Code 0 0 0 1 0 1 −0.5 0 5 10011 2 0 −0.5 5 10101 3 0.5 0 5 11001 4 −0.5 −0.5 5 11011 5 0 0.5 6 100100 6 0.5 −0.5 6 111000 7 0.5 0.5 6 111001 8 −0.5 0.5 6 111101 9 1 0 7 1011101 10 −1 0 7 1101000 11 0 −1 7 1110110 12 0 1 8 10010111 13 1 −0.5 8 10111101 14 −1 −0.5 8 11000111 15 1.5 0 8 11010110 16 −1 0.5 8 11101010 17 −0.5 −1 8 11101110 18 0.5 −1 8 11110000 19 −1.5 0 8 11110001 20 1 0.5 8 11111010 21 0 −1.5 9 100101010 22 0.5 1 9 100101100 23 −0.5 1 9 101000000 24 −1 −1 9 101001000 25 0 1.5 9 101100010 26 1 −1 9 101101001 27 −0.5 −1.5 9 101111100 28 −1.5 −0.5 9 101111110 29 2 0 9 110000001 30 1.5 −0.5 9 110000011 31 −1 1 9 110001010 32 0.5 −1.5 9 110001100 33 −2 0 9 110001101 34 1 1 9 110100110 35 0 −2 9 110101001 36 1.5 0.5 9 111100110 37 −1.5 0.5 9 111110000 38 −0.5 1.5 9 111110110 39 0.5 1.5 10 1001010011 40 0 2 10 1010001010 41 −2.5 0 10 1010010011 42 0 −2.5 10 1010010111 43 2.5 0 10 1010011100 44 0 −3.5 10 1011010100 45 0 2.5 10 1011010111 46 −2 −0.5 10 1011100000 47 2 −0.5 10 1011100111 48 −1 −1.5 10 1011111111 49 3 0 10 1100000000 50 −1.5 −1 10 1100001010 51 −0.5 −2 10 1100001100 52 0 3.5 10 1100001110 53 0 −3 10 1100010000 54 1.5 −1 10 1100010011 55 −3 0 10 1101001011 56 −1 −2 10 1101010000 57 0 3 10 1101011100 58 0.5 −2 10 1101011111 59 −2.5 −0.5 10 1110100110 60 −2 0.5 10 1110101100 61 1 −1.5 10 1110101110 62 −2 −1 10 1110101111 63 2 0.5 10 1110111101 64 −1.5 1 10 1110111111 65 −0.5 −2.5 10 1111100100 66 2 −1 10 1111100110 67 −3.5 0 10 1111101111 68 −0.5 2 10 1111110010 69 3.5 0 10 1111110100 70 1 −2 10 1111110111 71 1.5 1 10 1111111011 72 −2.5 0.5 10 1111111110 73 −1.5 −1.5 11 10010100100 74 −6.5 0 11 10010110101 75 0.5 −2.5 11 10010110111 76 −0.5 −3.5 11 10100001000 77 1.5 −1.5 11 10100001100 78 −0.5 2.5 11 10100001101 79 2.5 −0.5 11 10100010001 80 6.5 0 11 10100010111 81 2.5 0.5 11 10100011001 82 0.5 2.5 11 10100100101 83 −1 1.5 11 10100101010 84 −2 1 11 10100101100 85 0 −6.5 11 10100110000 86 0 −4 11 10100110110 87 1.5 1.5 11 10100111101 88 1 1.5 11 10100111110 89 −3.5 −0.5 11 10100111111 90 −1.5 1.5 11 10110000101 91 −3.5 0.5 11 10110000110 92 0.5 −3.5 11 10110000111 93 0.5 2 11 10110001101 94 −5.5 0 11 10110010111 95 5.5 0 11 10110011001 96 −0.5 3.5 11 10110100000 97 −4 0 11 10110100001 98 −1 2 11 10110101011 99 3 −0.5 11 10110110101 100 −3 −0.5 11 10110111000 101 −0.5 −3 11 10110111010 102 2 1 11 10110111011 103 3.5 0.5 11 10110111100 104 −9.5 0 11 10110111110 105 3 −1 11 10111000010 106 3 0.5 11 10111001000 107 0.5 3.5 11 10111001100 108 −14.5 0 11 10111001101 109 9.5 0 11 10111100100 110 4 0 11 10111100110 111 9 0 11 10111110101 112 −0.5 3 11 11000000010 113 3.5 −0.5 11 11000001010 114 5 0 11 11000010000 115 6 0 11 11000010001 116 4.5 0 11 11000010011 117 0 −9.5 11 11000100010 118 −3 −1 11 11000100100 119 −4.5 0 11 11000100101 120 −6 0 11 11000101110 121 −1 −3 11 11010100010 122 14.5 0 11 11010101001 123 −15.5 0 11 11010101011 124 0 −4.5 11 11010101100 125 0 6.5 11 11010101111 126 −5 0 11 11101000010 127 0 −14.5 11 11101000101 128 1 2 11 11101000110 129 8.5 0 11 11101001001 130 −3.5 −1.5 11 11101001010 131 3 1 11 11101001011 132 −11.5 0 11 11101001111 133 0 5.5 11 11101111100 134 −2 −1.5 11 11110010001 135 0.5 −3 11 11110010011 136 −2 −2 11 11110010100 137 0 −15.5 11 11110010101 138 −15 0 11 11110010110 139 0 −6 11 11110010111 140 −8.5 0 11 11110011101 141 −9 0 11 11110011110 142 −3 0.5 11 11110011111 143 15.5 0 11 11111000101 144 0 4 11 11111000111 145 11.5 0 11 11111001111 146 −3.5 1.5 11 11111011101 147 0.5 3 11 11111100001 148 −7 0 11 11111100011 149 2.5 −1 11 11111100111 150 −6.5 −0.5 11 11111101010 151 0 −5.5 11 11111101100 152 −2.5 −1 11 11111110000 153 0 −5 11 11111110010 154 −1 3 11 11111110100 155 −3 1 11 11111111010 156 0 6 12 100101000001 157 2.5 −1.5 12 100101000110 158 0 −9 12 100101001010 159 −0.5 −6.5 12 100101011001 160 2 −2 12 100101011010 161 −1.5 −2 12 100101011111 162 0 4.5 12 100101101000 163 −4 −0.5 12 100101101001 164 −3.5 1 12 100101101101 165 −4 −1 12 101000001010 166 0 5 12 101000001101 167 −6.5 0.5 12 101000010010 168 1 −3 12 101000010101 169 −1 −4 12 101000011100 170 −16 0 12 101000011110 171 −1 −2.5 12 101000011111 172 −3.5 −1 12 101000100101 173 1.5 −2 12 101000100111 174 2 −1.5 12 101000101100 175 3.5 −1.5 12 101000110110 176 −0.5 −4 12 101000110111 177 −4 1 12 101000111000 178 0 −11.5 12 101000111010 179 0 9.5 12 101000111100 180 3.5 1.5 12 101000111101 181 0 8.5 12 101001010000 182 −9.5 −0.5 12 101001010011 183 −4 0.5 12 101001011011 184 −10 0 12 101001100010 185 −2.5 1.5 12 101001100100 186 −4.5 0.5 12 101001101010 187 6.5 −0.5 12 101001110111 188 −5.5 0.5 12 101001111000 189 4.5 0.5 12 101100000001 190 0.5 −4 12 101100000100 191 3 −1.5 12 101100000101 192 −2.5 −1.5 12 101100000110 193 −2 1.5 12 101100001000 194 2.5 1 12 101100011001 195 6.5 0.5 12 101100011101 196 −5.5 −0.5 12 101100011110 197 −2.5 1 12 101100011111 198 1 3 12 101100100001 199 0 −8.5 12 101100100010 200 0.5 −6.5 12 101100100011 201 −7.5 0 12 101100100100 202 3 −2 12 101100100101 203 −10.5 0 12 101100101000 204 6 −0.5 12 101100101010 205 5.5 −0.5 12 101100101101 206 3.5 −1 12 101100110100 207 −4.5 −0.5 12 101100110110 208 2 2 12 101100111001 209 0 −15 12 101100111010 210 1 −2.5 12 101100111100 211 0 −7 12 101100111101 212 2.5 1.5 12 101100111110 213 0 9 12 101100111111 214 11 0 12 101101000101 215 −1 2.5 12 101101000110 216 −14.5 −0.5 12 101101000111 217 4 −1 12 101101010101 218 0.5 −4.5 12 101101011001 219 −9.5 0.5 12 101101011010 220 10.5 0 12 101101011011 221 5.5 0.5 12 101101100010 222 9.5 −0.5 12 101101100011 223 0 14.5 12 101101100101 224 4.5 −0.5 12 101101101000 225 3.5 1 12 101101101100 226 7.5 0 12 101101101110 227 −0.5 −9.5 12 101101101111 228 −8 0 12 101101110011 229 2 1.5 12 101101111011 230 −1.5 −2.5 12 101110000110 231 −2 2 12 101110000111 232 4 −0.5 12 101110001011 233 1 −4 12 101110001110 234 15 0 12 101110001111 235 −0.5 5.5 12 101110010010 236 −12 0 12 101110010011 237 1.5 2 12 101110010100 238 8 0 12 101110010111 239 −0.5 −4.5 12 101111000010 240 −11 0 12 101111000100 241 0 −16 12 101111000101 242 4 0.5 12 101111000110 243 −14.5 0.5 12 101111000111 244 −1 −3.5 12 101111001011 245 −0.5 −5.5 12 101111001110 246 0 −7.5 12 101111001111 247 7 0 12 101111101000 248 5 −1 12 101111101100 249 1.5 −2.5 12 101111101101 250 14 0 12 101111101110 251 −3 −2 12 101111111000 252 −11.5 −0.5 12 101111111001 253 0 −10 12 101111111011 254 0 11.5 12 110000000110 255 −7 −0.5 12 110000010010 256 −0.5 6.5 12 110000010011 257 −15.5 15.5 12 110000100100 258 13.5 0 12 110000100101 259 −15.5 −0.5 12 110000101101 260 −0.5 4.5 12 110000101110 261 5 −0.5 12 110000101111 262 −5 −0.5 12 110000110101 263 0.5 5.5 12 110000110110 264 −14 0 12 110000110111 265 0 −11 12 110000111100 266 0.5 −5.5 12 110000111110 267 −5 1 12 110001000110 268 −6 −0.5 12 110001000111 269 8.5 −0.5 12 110001011000 270 −1.5 2 12 110001011001 271 1 −3.5 12 110001011010 272 −1.5 2.5 12 110001011111 273 15.5 −0.5 12 110100100010 274 −0.5 −14.5 12 110100100011 275 14.5 −0.5 12 110100100101 276 −15.5 −15.5 12 110100101010 277 0.5 6.5 12 110100101011 278 1 2.5 12 110100111000 279 −13.5 0 12 110100111100 280 −4 −1.5 12 110100111101 281 15.5 −15.5 12 110100111110 282 0 −8 12 110100111111 283 4 1 12 110101000111 284 0 15.5 12 110101010000 285 3 1.5 12 110101010101 286 −5 0.5 12 110101011011 287 −5 −1 12 110101011100 288 1.5 2.5 12 110101011101 289 −2 −3 12 110101110100 290 −15.5 0.5 12 110101110110 291 −3 −1.5 12 110101110111 292 0 −14 12 110101111000 293 −8.5 −0.5 12 110101111010 294 −0.5 4 12 110101111011 295 9.5 0.5 12 111010000010 296 2.5 −2 12 111010000111 297 14.5 0.5 12 111010001000 298 −0.5 −6 12 111010001110 299 0.5 4.5 12 111010001111 300 −0.5 −15.5 12 111010010000 301 0 −12 12 111010010001 302 11.5 −0.5 12 111010011100 303 10 0 12 111010110110 304 −4 −2 12 111010110111 305 −15 −0.5 12 111011110010 306 −0.5 −11.5 12 111011111010 307 −1.5 −3.5 12 111011111011 308 1.5 3.5 12 111100100001 309 0 8 12 111100100101 310 9 −0.5 12 111100111000 311 −0.5 6 12 111110001001 312 −0.5 8.5 12 111110010100 313 −12.5 0 12 111110010101 314 2 −3 12 111110010111 315 8.5 0.5 12 111110011100 316 −8.5 0.5 12 111110011101 317 1.5 −3.5 12 111110111001 318 0.5 −9.5 12 111111000000 319 −2 3 12 111111000001 320 0 10.5 12 111111000100 321 −1 3.5 12 111111000101 322 0 7.5 12 111111001101 323 −3.5 −2 12 111111010110 324 6 −1 12 111111010111 325 −0.5 9.5 12 111111011011 326 −1.5 3.5 12 111111100111 327 0 13.5 12 111111101010 328 −0.5 14.5 12 111111101011 329 −2.5 −2.5 12 111111110000 330 1 4 12 111111110001 331 0.5 −5 12 111111110010 332 −2.5 −2 12 111111110011 333 −6 0.5 12 111111111100 334 0.5 4 12 111111111101 335 5 0.5 12 111111111110 336 15.5 0.5 12 111111111111 337 15.5 15.5 13 1001010000000 338 −3.5 −3.5 13 1001010000001 339 1 −5 13 1001010000100 340 3 2 13 1001010000111 341 −2 −2.5 13 1001010001000 342 −1 4 13 1001010001001 343 0 −10.5 13 1001010001010 344 −3 1.5 13 1001010001011 345 −11.5 0.5 13 1001010001111 346 −0.5 −5 13 1001010010111 347 −1 −5 13 1001010110111 348 0.5 8.5 13 1001010111000 349 −10 −0.5 13 1001010111010 350 −12 −0.5 13 1001010111011 351 0.5 −14.5 13 1001010111100 352 2.5 −2.5 13 1001010111101 353 −7 −1 13 1010000010000 354 −4.5 1.5 13 1010000010011 355 12.5 0 13 1010000010111 356 −0.5 5 13 1010000011000 357 0.5 −6 13 1010000011001 358 2.5 2.5 13 1010000011111 359 3 3 13 1010000100110 360 0 11 13 1010000101000 361 0 −13.5 13 1010000101101 362 −3 −3 13 1010000101110 363 11.5 0.5 13 1010000101111 364 −9 −0.5 13 1010000111010 365 −4 1.5 13 1010000111011 366 2 3 13 1010001000011 367 4 −2 13 1010001001000 368 −2 −4 13 1010001001001 369 0 14 13 1010001001100 370 2.5 2 13 1010001100010 371 −1.5 −3 13 1010001101000 372 0.5 9.5 13 1010001101001 373 −4.5 −1.5 13 1010001101011 374 4.5 −1 13 1010001110010 375 1.5 −3 13 1010001110111 376 −15 −1 13 1010001111100 377 −0.5 −8.5 13 1010010010010 378 −0.5 11.5 13 1010010010011 379 0.5 −15.5 13 1010010100011 380 −4.5 −1 13 1010010101100 381 6 0.5 13 1010010110101 382 0 7 13 1010011000110 383 5 1 13 1010011001101 384 10.5 −0.5 13 1010011010000 385 −2.5 2.5 13 1010011010001 386 −4.5 1 13 1010011010010 387 1 3.5 13 1010011010011 388 3 −3 13 1010011010110 389 5.5 −1 13 1010011011111 390 8 −0.5 13 1010011101000 391 −10.5 −0.5 13 1010011101001 392 3.5 2.5 13 1010011101010 393 4.5 −1.5 13 1010011101011 394 3.5 −2 13 1011000000000 395 −16 −1 13 1011000000100 396 −7.5 −0.5 13 1011000000101 397 −10.5 0.5 13 1011000000110 398 −0.5 −7 13 1011000000111 399 2 −4 13 1011000001110 400 −6 −1 13 1011000001111 401 −2.5 2 13 1011000010010 402 0.5 14.5 13 1011000010011 403 −16 −0.5 13 1011000110000 404 −3 2 13 1011000110001 405 12 0 13 1011000111000 406 −3.5 2.5 13 1011000111001 407 1.5 4.5 13 1011001000000 408 2 −2.5 13 1011001000001 409 0.5 −11.5 13 1011001001100 410 15 −0.5 13 1011001001101 411 −3.5 −2.5 13 1011001001110 412 −5.5 −1 13 1011001001111 413 −1 5 13 1011001010010 414 0 −12.5 13 1011001010011 415 0.5 11.5 13 1011001010110 416 2 2.5 13 1011001010111 417 −1 −6 13 1011001011000 418 1.5 3 13 1011001011001 419 −11 −0.5 13 1011001100000 420 13 0 13 1011001100001 421 −5.5 1.5 13 1011001100010 422 −6 1 13 1011001100011 423 −0.5 −15 13 1011001101010 424 −3.5 3.5 13 1011001101011 425 −0.5 −16 13 1011001101110 426 4.5 1 13 1011001101111 427 −7.5 0.5 13 1011001110000 428 −0.5 −9 13 1011001110001 429 −10 −1 13 1011001110110 430 3 −4 13 1011001110111 431 4 −1.5 13 1011010001000 432 −1 −7 13 1011010001001 433 0.5 6 13 1011010101000 434 −13 0 13 1011010101001 435 11 −0.5 13 1011010110000 436 1 −6 13 1011010110001 437 14 −0.5 13 1011011000000 438 3.5 3.5 13 1011011000001 439 −0.5 −7.5 13 1011011000010 440 −14.5 −14.5 13 1011011000011 441 −0.5 9 13 1011011001000 442 −7 0.5 13 1011011001001 443 3.5 −3.5 13 1011011001100 444 −15.5 −1.5 13 1011011001101 445 −1 −4.5 13 1011011001110 446 −1.5 3 13 1011011001111 447 −4 3 13 1011011010010 448 −2 2.5 13 1011011010011 449 7.5 −0.5 13 1011011011010 450 3 −2.5 13 1011011011011 451 −2.5 −3.5 13 1011011100100 452 0.5 5 13 1011011100101 453 7 −0.5 13 1011011110100 454 −15 0.5 13 1011011110101 455 −14 −0.5 13 1011011111100 456 7.5 0.5 13 1011011111101 457 4.5 1.5 13 1011011111110 458 −3 3 13 1011011111111 459 −3 −2.5 13 1011100010000 460 −1.5 −4.5 13 1011100010001 461 −5.5 1 13 1011100010010 462 −4 2 13 1011100010011 463 1 −4.5 13 1011100010100 464 −14.5 14.5 13 1011100010101 465 −2 4 13 1011100011000 466 −12 −1 13 1011100011001 467 −0.5 15.5 13 1011100011010 468 −4 −3 13 1011100011011 469 2.5 −3 13 1011100101010 470 14.5 −14.5 13 1011100101011 471 −8 −0.5 13 1011100101100 472 9 −1 13 1011100101101 473 0 10 13 1011110000000 474 1 5 13 1011110000001 475 1.5 −4 13 1011110000010 476 −0.5 −10 13 1011110000011 477 0 15 13 1011110000110 478 −1 −5.5 13 1011110000111 479 5 −2 13 1011110010100 480 1.5 −4.5 13 1011110010101 481 −2 −3.5 13 1011111010010 482 3 −3.5 13 1011111010011 483 −1.5 4.5 13 1011111011110 484 3.5 −2.5 13 1011111011111 485 −5 −1.5 13 1011111110100 486 −1 4.5 13 1011111110101 487 −1 6 13 1100000001110 488 13.5 −0.5 13 1100000001111 489 −5 −2 13 1100000100000 490 9 0.5 13 1100000100001 491 −11 −1 13 1100000100010 492 1 4.5 13 1100000100011 493 −0.5 10.5 13 1100000101100 494 −5.5 −1.5 13 1100000101101 495 14 −1 13 1100000101110 496 −9 −1 13 1100000101111 497 −4 −4 13 1100001011000 498 2.5 −3.5 13 1100001011001 499 0.5 10.5 13 1100001101000 500 2.5 3.5 13 1100001101001 501 15.5 −1.5 13 1100001111010 502 5.5 −1.5 13 1100001111011 503 4 1.5 13 1100001111110 504 13.5 0.5 13 1100001111111 505 5.5 1 13 1100010110110 506 −3.5 2 13 1100010110111 507 3.5 2 13 1100010111100 508 −1.5 −4 13 1100010111101 509 10.5 0.5 13 1101001000000 510 −1.5 4 13 1101001000001 511 1 −5.5 13 1101001000010 512 −0.5 13.5 13 1101001000011 513 0.5 −8.5 13 1101001001000 514 −0.5 11 13 1101001001001 515 8 0.5 13 1101001001100 516 −0.5 −12 13 1101001001101 517 −0.5 8 13 1101001001110 518 −8 0.5 13 1101001001111 519 −0.5 −10.5 13 1101001010000 520 10 −0.5 13 1101001010001 521 −15.5 1.5 13 1101001010010 522 −13.5 0.5 13 1101001010011 523 −9.5 −3.5 13 1101001110010 524 0 12.5 13 1101001110011 525 −0.5 7.5 13 1101001110100 526 14.5 14.5 13 1101001110101 527 0.5 −7.5 13 1101001110110 528 0.5 −7 13 1101001110111 529 −0.5 −13.5 13 1101010001100 530 −4 −3.5 13 1101010001101 531 −1.5 −15.5 13 1101010100010 532 1 −7 13 1101010100011 533 −1 −15 13 1101010101000 534 −1.5 −5.5 13 1101010101001 535 12.5 −15.5 13 1101010110100 536 5 −1.5 13 1101010110101 537 8 −1 13 1101011101010 538 −3.5 −3 13 1101011101011 539 −6.5 −1 13 1101011110010 540 2.5 3 13 1101011110011 541 −3 −3.5 13 1110100000000 542 −13.5 −0.5 13 1110100000001 543 0.5 −10.5 13 1110100000010 544 −8 −1 13 1110100000011 545 −3 −4 13 1110100000110 546 −6.5 3.5 13 1110100000111 547 −16 0.5 13 1110100001100 548 −1 5.5 13 1110100001101 549 15.5 1.5 13 1110100010010 550 0.5 13.5 13 1110100010011 551 3.5 3 13 1110100111010 552 2 −3.5 13 1110100111011 553 −2.5 −3 13 1110101101000 554 3 2.5 13 1110101101001 555 −16 1 13 1110101101010 556 15 −1 13 1110101101011 557 4 2 13 1110111100000 558 10 −1 13 1110111100001 559 −2.5 3.5 13 1110111100010 560 −1 −10 13 1110111100011 561 0.5 15.5 13 1110111100110 562 −9 0.5 13 1110111100111 563 11 −1 13 1111001000000 564 −3.5 −9.5 13 1111001000001 565 −0.5 −11 13 1111001001000 566 3 4 13 1111001001001 567 7 0.5 13 1111001110010 568 −10 0.5 13 1111001110011 569 −3 2.5 13 1111100010000 570 7 −1 13 1111100010001 571 −6.5 −15.5 13 1111100011000 572 −3.5 3 13 1111100011001 573 −2 −5 13 1111100011010 574 −6 −1.5 13 1111100011011 575 0 −13 13 1111100101100 576 1.5 −5.5 13 1111100101101 577 −0.5 14 13 1111101110000 578 −6.5 −3.5 13 1111101110001 579 −15.5 −1 13 1111110011000 580 −12.5 −0.5 13 1111110011001 581 5 2 13 1111110110100 582 1.5 5.5 13 1111110110101 583 3 3.5 13 1111111000100 584 4 3 13 1111111000101 585 13 −0.5 13 1111111000110 586 −5 1.5 13 1111111000111 587 −1 −6.5 13 1111111001100 588 0 13 13 1111111001101 589 12.5 −0.5 13 1111111101100 590 15 −15.5 13 1111111101101 591 −0.5 −8 13 1111111101110 592 −14.5 −5.5 13 1111111101111 593 14.5 −5.5 14 10010100001010 594 −11.5 11.5 14 10010100001011 595 1.5 4 14 10010100001100 596 12.5 15.5 14 10010100001101 597 3.5 −4 14 10010100011100 598 0 12 14 10010100011101 599 −4 −2.5 14 10010100101100 600 −11.5 −11.5 14 10010100101101 601 2 −6 14 10010101100000 602 −1.5 15.5 14 10010101100001 603 −16 −2 14 10010101100010 604 4.5 −2.5 14 10010101100011 605 −15.5 3.5 14 10010101101100 606 −9.5 −1 14 10010101101101 607 −0.5 7 14 10010101110010 608 −14.5 4.5 14 10010101110011 609 5 −3 14 10010110110000 610 −3.5 −4.5 14 10010110110001 611 4 −4 14 10010110110010 612 0.5 −9 14 10010110110011 613 −15 −15 14 10100000100010 614 1 5.5 14 10100000100011 615 −14.5 −1 14 10100000100100 616 −15 −15.5 14 10100000100101 617 5.5 3.5 14 10100000101100 618 −5.5 −14.5 14 10100000101101 619 −1.5 5.5 14 10100000111000 620 −11 0.5 14 10100000111001 621 0.5 −13.5 14 10100000111010 622 −12.5 0.5 14 10100000111011 623 −0.5 −14 14 10100000111100 624 15 0.5 14 10100000111101 625 −6 −3 14 10100001001110 626 4.5 −2 14 10100001001111 627 −4 2.5 14 10100001010010 628 −14.5 5.5 14 10100001010011 629 14.5 4.5 14 10100001011000 630 5.5 1.5 14 10100001011001 631 −15 −5 14 10100010000000 632 0.5 −10 14 10100010000001 633 −2 −6 14 10100010000010 634 −1 9 14 10100010000011 635 13.5 −15.5 14 10100010000100 636 −9.5 −9.5 14 10100010000101 637 −15.5 8.5 14 10100010011010 638 −14 −1 14 10100010011011 639 10 0.5 14 10100010110100 640 2 −5 14 10100010110101 641 15.5 −6.5 14 10100010110110 642 2 4 14 10100010110111 643 −1 −12 14 10100011000000 644 0.5 7.5 14 10100011000001 645 0.5 −16 14 10100011000010 646 −14.5 10.5 14 10100011000011 647 6.5 −3.5 14 10100011000110 648 −1.5 5 14 10100011000111 649 1 6 14 10100011010100 650 −0.5 15 14 10100011010101 651 6.5 −1 14 10100011100110 652 11.5 11.5 14 10100011100111 653 −14.5 −15.5 14 10100011101100 654 9.5 −9.5 14 10100011101101 655 −2 3.5 14 10100011111010 656 15.5 −14.5 14 10100011111011 657 0.5 −15 14 10100011111100 658 0.5 −8 14 10100011111101 659 14.5 −15.5 14 10100011111110 660 6 3 14 10100011111111 661 −6 −2 14 10100100100000 662 11 0.5 14 10100100100001 663 −4.5 2.5 14 10100100100010 664 0.5 8 14 10100100100011 665 −5.5 3.5 14 10100101000100 666 11.5 −11.5 14 10100101000101 667 13.5 −14.5 14 10100101001000 668 6.5 −15.5 14 10100101001001 669 −14.5 9.5 14 10100101001010 670 6.5 3.5 14 10100101001011 671 15.5 −11.5 14 10100101011010 672 −5 −4 14 10100101011011 673 5 1.5 14 10100101011100 674 3 −5 14 10100101011101 675 −1 −15.5 14 10100101011110 676 −9.5 3 14 10100101011111 677 4.5 2.5 14 10100101101000 678 −6.5 2.5 14 10100101101001 679 1.5 −5 14 10100110001110 680 15.5 −4.5 14 10100110001111 681 −15.5 14.5 14 10100110010100 682 −3.5 −4 14 10100110010101 683 −15 1 14 10100110010110 684 2 5 14 10100110010111 685 3.5 8.5 14 10100110011000 686 −5 3 14 10100110011001 687 −11.5 −3.5 14 10100110011100 688 −9 −3 14 10100110011101 689 −6 2 14 10100110011110 690 1.5 6.5 14 10100110011111 691 −14.5 −10.5 14 10100110101110 692 5.5 −3.5 14 10100110101111 693 −12.5 −15.5 14 10100110111000 694 −4.5 −3.5 14 10100110111001 695 −4.5 −2.5 14 10100110111010 696 −9.5 3.5 14 10100110111011 697 −14.5 15.5 14 10100110111100 698 9.5 8.5 14 10100110111101 699 6.5 2.5 14 10100111011000 700 −1.5 −6.5 14 10100111011001 701 −10 −3 14 10100111011010 702 −11.5 3.5 14 10100111011011 703 −2.5 3 14 10100111100100 704 −2 5 14 10100111100101 705 −5.5 −3.5 14 10100111100110 706 9.5 3.5 14 10100111100111 707 1.5 −15.5 14 10110000000010 708 6 1 14 10110000000011 709 Esc Esc 4 1000 @ Brief Overview of a Computer System

FIG. 7 and the following discussion are intended to provide a brief, general description of a suitable computing environment in which the invention may be implemented. Although the invention or aspects of it may be implemented in a hardware device, the encoder and decoder described above are implemented in computer-executable instructions organized in program modules. The program modules include the routines, programs, objects, components, and data structures that perform the tasks and implement the data types described above.

While FIG. 7 shows a typical configuration of a desktop computer, the invention may be implemented in other computer system configurations, including hand-held devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, minicomputers, mainframe computers, and the like. The invention may also be used in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

FIG. 7 illustrates an example of a computer system that serves as an operating environment for the invention. The computer system includes a personal computer 720, including a processing unit 721, a system memory 722, and a system bus 723 that interconnects various system components including the system memory to the processing unit 721. The system bus may comprise any of several types of bus structures including a memory bus or memory controller, a peripheral bus, and a local bus using a bus architecture such as PCI, VESA, Microchannel (MCA), ISA and EISA, to name a few. The system memory includes read only memory (ROM) 724 and random access memory (RAM) 725. A basic input/output system 726 (BIOS), containing the basic routines that help to transfer information between elements within the personal computer 720, such as during start-up, is stored in ROM 724. The personal computer 720 further includes a hard disk drive 727, a magnetic disk drive 728, e.g., to read from or write to a removable disk 729, and an optical disk drive 730, e.g., for reading a CD-ROM disk 731 or to read from or write to other optical media. The hard disk drive 727, magnetic disk drive 728, and optical disk drive 730 are connected to the system bus 723 by a hard disk drive interface 732, a magnetic disk drive interface 733, and an optical drive interface 734, respectively. The drives and their associated computer-readable media provide nonvolatile storage of data, data structures, computer-executable instructions (program code such as dynamic link libraries, and executable files), etc. for the personal computer 720. Although the description of computer-readable media above refers to a hard disk, a removable magnetic disk and a CD, it can also include other types of media that are readable by a computer, such as magnetic cassettes, flash memory cards, digital video disks, Bernoulli cartridges, and the like.

A number of program modules may be stored in the drives and RAM 725, including an operating system 735, one or more application programs 736, other program modules 737, and program data 738. A user may enter commands and information into the personal computer 720 through a keyboard 740 and pointing device, such as a mouse 742. Other input devices (not shown) may include a microphone, joystick, game pad, satellite dish, scanner, or the like. These and other input devices are often connected to the processing unit 721 through a serial port interface 746 that is coupled to the system bus, but may be connected by other interfaces, such as a parallel port, game port or a universal serial bus (USB). A monitor 747 or other type of display device is also connected to the system bus 723 via an interface, such as a display controller or video adapter 748. In addition to the monitor, personal computers typically include other peripheral output devices (not shown), such as speakers and printers.

The personal computer 720 may operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 749. The remote computer 749 may be a server, a router, a peer device or other common network node, and typically includes many or all of the elements described relative to the personal computer 720, although only a memory storage device 750 has been illustrated in FIG. 7. The logical connections depicted in FIG. 7 include a local area network (LAN) 751 and a wide area network (WAN) 752. Such networking environments are commonplace in offices, enterprise-wide computer networks, intranets and the Internet.

When used in a LAN networking environment, the personal computer 720 is connected to the local network 751 through a network interface or adapter 753. When used in a WAN networking environment, the personal computer 720 typically includes a modem 754 or other means for establishing communications over the wide area network 752, such as the Internet. The modem 754, which may be internal or external, is connected to the system bus 723 via the serial port interface 746. In a networked environment, program modules depicted relative to the personal computer 720, or portions thereof, may be stored in the remote memory storage device. The network connections shown are merely examples and other means of establishing a communications link between the computers may be used.

CONCLUSION

While the invention has been illustrated using a specific implementation as an example, the scope of the invention is not limited to the specific implementation described above. Spatial prediction effectively exploits the spatial dependency of motion vectors and improves the efficiency of jointly coding motion vectors with a single entropy code. However, the specific form of prediction used on the motion vectors is not critical to the invention. In fact, it is possible to implement the invention without using a prediction scheme.

The implementation described above specifically uses a Huffman coding scheme to compute entropy codes for a joint motion vector parameter. As noted, it is also possible to use other forms of entropy coding to encode the joint parameter with a single entropy code.

In view of the many possible implementations of the invention, it should be recognized that the implementation described above is only examples of the invention and should not be taken as a limitation on the scope of the invention. Rather, the scope of the invention is defined by the following claims. We therefore claim as our invention all that comes within the scope and spirit of these claims. 

1. In a video coder for coding video images in a block format, a method for improving compression of the video images comprising: predicting x and y motion vector components for a current block of pixels based on a motion vector of at least one neighboring block of pixels to compute x and y components of a predictor motion vector; computing differential x and y components from the x and y components of the predictor and x and y components of a motion vector for the current block; and assigning a single variable length code to joint x and y differential motion vector components, wherein the single variable length code is assigned from a variable length code table, the table comprising a list of pairs of joint differential motion vector components and a corresponding variable length code for each pair, such that shorter variable length codes are assigned to joint differential motion vector components that have a higher probability of occurrence in the video images, and longer variable length codes are assigned to joint differential motion vector components that have a lower probability of occurrence, wherein the table includes the most probable pairs of joint differential motion vector components as computed by statistical analysis of example video sequences.
 2. The method of claim 1 wherein the assigning includes: looking up the joint differential motion vector components in the table; when no match is found in the table, coding an escape code along with a fixed length code for each differential motion vector component.
 3. The method of claim 1 wherein the block of pixels corresponds to a macroblock in a video frame divided into fixed-sized, rectangular macroblocks, and the predicting, computing, and assigning are repeated for the macroblocks in the video frame.
 4. The method of claim 1 wherein the block of pixels corresponds to a macroblock of a video object plane in a video frame having two more video object planes, and the video object planes are each divided into fixed-sized, rectangular macroblocks; and the predicting, computing and assigning are repeated for the macroblocks in the video object planes.
 5. A computer readable medium having instructions for performing the method of claim
 1. 6. In a video decoder, a method for decoding macroblocks of a predicted video frame comprising: receiving a single variable length code representing joint x and y components of a motion vector for each of the macroblocks; for each of the macroblocks, searching for a single entry in an entropy codebook corresponding to the variable length code and including the x and y components of the motion vector, wherein training determines which x and y components to include in the entropy codebook; and using the x and y components of the motion vector from the codebook to define motion of pixels in a corresponding macroblock.
 7. The method of claim 6 wherein the x and y components of the motion vector in the codebook comprise x and y differential motion vector components, and the method comprises: reconstructing the motion vector from the differential motion vector components and x and y components of a predictor motion vector.
 8. The method of claim 6 wherein the codebook is a Huffman table trained for a target bit rate and content type from a statistical analysis of example video sequences having the content type.
 9. A computer readable medium having instructions for performing the method of claim
 6. 10. A motion vector encoder comprising: a motion vector predictor for computing a motion vector predictor for a motion vector of a block of pixels from at least one motion vector for a neighboring block of pixels; a subtractor for computing differential motion vector components from motion vector components of the predictor and the motion vector of the block of pixels; and a joint entropy coder for jointly coding the differential motion vector components with a single variable length code, wherein statistical analysis indicates which differential motion vector components to represent with variable length codes and which differential motion vector components to represent with an escape code followed by fixed length codes.
 11. The encoder of claim 10 wherein the joint entropy coder computes the single variable length code by searching for the code in a Huffman coding table comprising a list of joint differential motion vectors and a corresponding variable length code for each of the joint differential motion vectors.
 12. A motion vector decoder comprising: a motion vector predictor for computing a motion vector predictor for a motion vector of a block of pixels from at least one motion vector for a neighboring block of pixels; a joint entropy decoder for decoding a single variable length code into joint differential motion vector components, wherein the joint entropy decoder decodes the single variable length code by searching for the code in a Huffman coding table comprising a list of variable length codes and corresponding joint differential motion vector components for each of the variable length codes, wherein training determines which joint differential motion vector components to include in the table and which joint differential motion vector components to exclude from the table; and an adder for reconstructing X and Y motion vector components from the joint differential motion vector components and X and Y components of the motion vector predictor.
 13. The decoder of claim 12 wherein the joint entropy decoder is operable to detect an escape code indicating that two fixed length codes representing X and Y differential motion vector components follow the escape code.
 14. In a video coder for coding video images in a block format, a method for improving compression of the video images comprising: computing x and y motion vector components for a block; forming the x and y motion vector components into a joint parameter representing joint x and y motion vector components; and assigning a single variable length code to the joint x and y motion vector components, the single variable length code selected from a set of available variable length codes, such that shorter variable length codes are assigned to joint motion vector components that have a higher probability of occurrence in the video images, and longer variable length codes are assigned to joint differential motion vector components that have a lower probability of occurrence, wherein training determines which joint x and y motion vector components to represent in the set of available variable length codes.
 15. The method of claim 14 further including spatially predicting the x and y motion vector components from a neighboring block of the block; and using spatially predicted components as the joint x and y motion vector components.
 16. The method of claim 15 wherein the spatially predicted components are differential motion vector components computed as a difference between x and y components of the motion vector for the block and x and y components of a predictor motion vector.
 17. In a video decoder, a method for decoding macroblocks of a predicted video frame comprising: receiving a single variable length code representing joint differential x and y components of a motion vector for each of the macroblocks; for each of the macroblocks, searching for a single entry in a Huffman table corresponding to the variable length code and including the joint differential x and y components of the motion vector, wherein the Huffman table includes variable length codes for the most probable joint differential x and y components as computed by statistical analysis of example video sequences; computing x and y components of a predictor motion vector from neighboring macroblocks to the macroblock currently being decoded; and reconstructing the motion vector from the differential components obtained from the Huffman table and the x and y components of the predictor motion vector.
 18. In a video coder for coding video images in a block format, a method for variable length coding block motion information of the video images, wherein a joint parameter represents x and y motion vector components for a block, the method comprising: assigning a single variable length code selected from a set of available variable length codes to the joint x and y motion vector components, wherein training determines which joint x and y motion vector components to represent in the set of available variable length codes.
 19. The method of claim 18 wherein the block is a 16×16 macroblock of pixels, and wherein each of the x and y motion vector components comprises a differential value.
 20. A video decoder including computer-executable instructions for causing a computer programmed thereby to perform a method for variable length decoding macroblock motion information of a predicted video frame, wherein a single variable length code represents joint differential x and y components of a motion vector for each of plural macroblocks, the method comprising: for each of the plural macroblocks, searching for a single entry in a Huffman table corresponding to the variable length code for the macroblock, wherein the single entry includes the joint differential x and y components of the motion vector for the macroblock, wherein the joint differential x and y components are combinable with predictor x and y components to reconstruct the motion vector for the macroblock, and wherein the Huffman table includes variable length codes for the most probable joint differential x and y components as computed by statistical analysis of example video sequences. 